What/who decides who's verified and who's not? Is it case of being registered with the IBJJF or something? I've recently started training with Crazy Monkeys and I didn't see them mentioned once on the list?

Oh right, I remember... wasn't there some nonsense about "Monkey Jitz" before?? It's BJJ but it's not BJJ?! Something like that iirc.

It's just their BJJ association. The website is full of stuff about competition being secondary to self actualisation, or something, but their lineage is legit.

so should I run for the hills or? Would any possible promotion (I'm hoping they let me wear a white belt soon) be null and void?

You don't have to earn a white belt in BJJ, everyone's a white belt until someone gives them a blue one. Where's Phil's gym? He's on the Crazy Monkey trainer list but I can't find anything on the internet about him being a BJJ black belt.